Help me solve this

[mrtoan9x]

If a ball is thrown into the air with a velocity of 120ft/s, its height (in ft) after t seconds is given by h = 120t − 11t^2. Find the velocity when t = 4.

---

thank you

 

[lev888]

If a ball is thrown into the air with a velocity of 120ft/s, its height (in ft) after t seconds is given by h = 120t − 11t^2. Find the velocity when t = 4.

---

thank you

How do you get the rate of change function from the height fiction?

 

[Steven G]

I know this one! The avg velocity is the change in distance (height!) divided by the change in time. The instantaneous velocity is... ah, I thought I knew this. Oh well. Maybe you can figure it out on your own

 

[HallsofIvy]

If a ball is thrown into the air with a velocity of 120ft/s, its height (in ft) after t seconds is given by h = 120t − 11t^2. Find the velocity when t = 4.

---

thank you

As Jomo said above the average velocity over a time interval is "change in distance (height!) divided by the change in time". The instantaneous velocity is the limit of that as the length of the time interval goes to 0. The "limit concept" is crucial to the derivative.

Here the average velocity, between times t and t+ dt is (h(t+ dt)- h(t))/dt. h(t)= 120t- 11t^2 and h(t+ dt)= 120(t+ dt)- 11(t+ dt)^2= 120t+ 120dt- 11(t^2+ 2tdt+ dt^2)= 120t+ 120dt- 11t^2- 22tdt- 11dt^2.


h(t+ dt)- h(t)= 120dt- 22tdt- 11dt^2


(h(t+ dt)- h(t))/dt= 120- 22t-11dt

And the limit as dt goes to 0 is 120- 22t.